Chapter Nine: Simple Machines
9.1 Types of Simple Machines
9.2 Mechanical Advantage
9.3 Levers in the Human Body
9.1 Using Machines
A machine is a device
with moving parts
that work together to
accomplish a task.
A bicycle is a good
example.
9.1 Using Machines
The input includes everything you do to
make the machine accomplish a task, like
pushing on the bicycle pedals.
The output is what the machine does for
you, like going fast or climbing a steep hill.
9.1 Forces in Machines
A simple machine is an unpowered
mechanical device, such as a lever.
9.1 Review of work
 Every process that is done by machines can
be simplified in terms of work:
1. work input: the work or energy supplied to
the process (or machine).
2. work output: the work or energy that comes
out of the process (or machine).
9.1 Review of energy
A rope and pulley
machine illustrates a
rule that is true for all
processes that
transform energy.
The total energy or
work output can never
be greater than the total
energy or work input.
9.2 Mechanical advantage
Mechanical advantage is the ratio of
output force to input force.
9.2 Mechanical advantage
Machines multiply
forces.
One person could lift
an elephant—quite a
heavy load—with a
properly designed
system of ropes and
pulleys!
9.1 Mechanical Advantage
mechanical
advantage
MA = Fo
Fi
Input force (N)
Output force (N)
9.2 The Lever
A lever includes a stiff structure (the
lever) that rotates around a fixed point
called the fulcrum.
9.2 The Lever
Levers are useful because you can
arrange the fulcrum and the input arm
and output arm to adjust the
mechanical advantage of the lever.
9.2 The Lever
Each class of levers is defined by the
location of the input and output forces
relative to the fulcrum.
9.2 Gears
Many machines
require that rotating
motion be transmitted
from one place to
another.
Gears change force
and speed.
9.2 Designing Gear Machines
The gear ratio is the ratio of output turns
to input turns.
You can predict how force and speed are
affected when gears turn by knowing the
number of teeth for each gear.
9.2 Gear Ratios
Turns of output gear
Turns of input gear
To = Ni
Ti
No
Number of teeth
on input gear
Number of teeth
on input gear
9.2 Tension
Ropes and strings carry tension forces
along their length.
If the rope is not moving, its tension is
equal tothe force pulling on each end.
9.2 Ramps
A ramp is a simple machine that allows
you to raise a heavy object with less force
than you would need to lift it straight up.
The mechanical
advantage of a
ramp is the ramp
length divided by
the height of the
ramp.
9.2 Screws
A screw is a
rotating ramp.
You find the
mechanical
advantage of a
screw by dividing
its circumference
by the lead.
9.2 Screws
A wedge is like a ramp that
can work while in motion (a
ramp is always stationary).
A wedge has a side that
slopes down to a thin edge.
The mechanical advantage
for a wedge is inversely
related to the size of the
wedge angle.
9.2 Wheel and axle
A wheel rotates around a
rod called an axle.
The mechanical advantage
is the ratio of the radius of
the wheel to the radius of
the axle.
The wheel and axle move
together to move or lift
loads.
Solving Problems
A crowbar is a
type of lever that
you use to pull a
nail out of a piece
of wood.
If the handle of a crowbar is 40
centimeters and the foot is 2
centimeters, what is its mechanical
advantage?
Solving Problems
1. Looking for:
 …mechanical advantage of lever
2. Given
 …input arm = 40 cm; output arm = 2 cm
3. Relationships:
 M.A. = Length of input arm
Length of output arm
4. Solution
 M.A. = 40 cm ÷ 2 cm = 20
9.3 Levers in the human body
The human body is
a complex machine
that includes a
number of simple
machines—levers.
Your arms and legs,
for example, work
as levers to move
and lift objects.
9.3 Levers in the human body
A classic example of a
third class lever is a
broom.
A broom does not
multiply force, but it
does multiply speed.
Since your limbs are
third class levers, they
multiply speed to do
tasks quickly.
9.3 Levers in the human body
Human arms and legs
are examples of third
class levers because
the input forces are
between a fulcrum and
the output force.
The output force is
what you accomplish
with your hands and
feet.
Where is the input
force and the fulcrum?
9.3 Levers in the human body
In the human body, all bones act as
levers and each joint can serve as a
fulcrum.
 When lifting your head, your neck works as
a first-class lever.
 When you stand on your toes, the feet act
as second-class levers.
 When biting, your jaw works as a thirdclass lever.
8.2 Efficiency and Power
 Every process that is done by machines can
be simplified in terms of work:
1. work input: the work or energy supplied to
the process (or machine).
2. work output: the work or energy that comes
out of the process (or machine).
8.2 Efficiency and Power
A rope and pulley
machine illustrates a
rule that is true for all
processes that
transform energy.
The total energy or
work output can never
be greater than the total
energy or work input.
8.2 Efficiency
65% of the energy in
gasoline is converted
to heat.
As far as moving the
car goes, this heat
energy is “lost”.
The energy doesn’t
vanish, it just does
not appear as useful
output work.
8.2 Efficiency
The efficiency of a machine is the
ratio of usable output work divided by
total input work.
Efficiency is usually expressed in
percent.
Output work (J)
efficiency = Wo
Wi
Input work (J)
x 100%
Solving Problems
 You see a newspaper advertisement for a
new, highly efficient machine. The
machine claims to produce 2,000 joules of
output work for every 2,100 joules of
input work.
 What is the efficiency of this machine?
 Is it as efficient as a bicycle?
 Do you believe the advertisement’s claim?
Why or why not?
Solving Problems
1. Looking for:
 …efficiency of machine
2. Given:
 …Wi = 2100 J, Wo = 2000 J
3. Relationships:
 % efficiency = Wo x 100
Wi
4. Solution
 2000 J ÷ 2100 J x 100 = 95% efficient
8.2 Power
The rate at which work is done is
called power.
It makes a difference how fast you
do work.
8.2 Power
Michael and Jim do
the same amount of
work.
Jim’s power is
greater because he
gets the work done in
less time.
8.2 Power
Power is calculated in watts.
One watt (W) is equal to 1 joule of work per
second.
James Watt, a Scottish engineer, invented
the steam engine.
Jame Watt explained power as the number
of horses his engine could replace.
One horsepower still equals 746 watts.
8.2 Power
Work (joules)
Power (watts)
P =W
t
Time (s)
Solving Problems
 Allen lifts his weight
(500 newtons) up a
staircase that is 5 meters
high in 30 seconds.
 How much power does
he use?
 How does his power
compare with a 100-watt
light bulb?
Solving Problems
1. Looking for:
 …power
2. Given:
 Fweight= 500 N; d = 5 m, t = 30 s
3. Relationships:
 W = F x d; P = W ÷ t
4. Solution
 W = 500 N x 5 m = 2500 Nm
 P = 2500 Nm ÷ 30 s = 83 watts
 Allen’s power is less than a 100-watt light bulb.